Theorems · Definition · linear algebra

Module.Basis.sumExtend

{ι : Type u_1} →
  {K : Type u_3} →
    {V : Type u_4} →
      [inst : DivisionRing K] →
        [inst_1 : AddCommGroup V] →
          [inst_2 : Module K V] →
            {v : ι → V} → (hs : LinearIndependent K v) → Module.Basis (ι ⊕ ↑(Module.Basis.sumExtendIndex hs)) K V

If v is a linear independent family of vectors, extend it to a basis indexed by a sum type.

Defined in

Mathlib.LinearAlgebra.Basis.VectorSpace

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModule